The most commonly used method for displaying high-resolution images on a lower resolution display is to sample the pixels 2 of the high-resolution image 4 down to the resolution of the low-resolution display 6, as shown in FIG. 1. Then, the R, G, B values of each downsampled color pixel 8 are mapped to the separate R, G, B elements 10, 12 and 14 of each display pixel 16. These R, G, B elements 10, 12 and 14 of a display pixel are also referred to as subpixels. Because the display device does not allow overlapping color elements, the subpixels can only take on one of the three R, G, or B colors, however, the color's amplitude can be varied throughout the entire greyscale range (e.g., 0–255). The subpixels usually have a 1:3 aspect ratio (width:height), so that the resulting pixel 16 is square. The subsampling/mapping techniques do not consider the fact that the display's R, G, and B subpixels are spatially displaced; in fact they are assumed to be overlapping in the same manner as they are in the high-resolution image. This type of sampling may be referred to as sub-sampling or traditional sub-sampling.
The pixels of the high-resolution image 4 are shown as three slightly offset stacked squares 8 to indicate their RGB values are associated for the same spatial position (i.e., pixel). One display pixel 16, consisting of one each of the R, G and B subpixels 10, 12 and 14 is shown as part of the lower-resolution triad display 6 in FIG. 1 using dark lines. Other display pixels are shown with lighter gray lines.
In this example, the high-resolution image has 3× more resolution than the display (in both horizontal and vertical dimensions). Since this direct subsampling technique causes aliasing artifacts, various methods are used, such as averaging the neighboring unsampled pixels in with the sampled pixel. Note that the common technique of averaging neighboring elements while subsampling is mathematically equal to prefiltering the high resolution image with a rectangular (rect) filter. Also, note that techniques of selecting a different pixel than the leftmost (as shown in this figure) can be considered as a prefiltering that affects only phase. Thus, most of the processing associated with preventing aliasing can be viewed as a filtering operation on the high-resolution image, even if the kernel is applied only at the sampled pixel positions.
It has been realized that the aforementioned technique does not take advantage of potential display resolution. Background information in this area may be accessed by reference to R. Fiegenblatt (1989), “Full color imaging on amplitude color mosaic displays” Proc. SPIE V. 1075, 199–205; and J. Kranz and L. Silverstein (1990) “Color matrix display image quality: The effects of luminance and spatial sampling,” SID Symp. Digest 29–32 which are hereby incorporated herein by reference.
For example, in the display shown in FIG. 1, while the display pixel 16 resolution is ⅓ that of the high resolution image (source image) 4, the subpixels 10, 12 and 14 are at a resolution equal to that of the source (in the horizontal dimension). If this display were solely to be used by colorblind individuals, it would be possible to take advantage of the spatial positions of the subpixels. This approach is shown in FIG. 2 below, where the R, G, and B subpixels 10, 12 and 14 of the display are taken from the corresponding colors of different pixels 11, 13 and 15 of the high-resolution image. This allows the horizontal resolution to be at the subpixel resolution, which is 3× that of the display pixel resolution.
But what about the viewer of the display who is not color-blind? That is, the majority of viewers. Fortunately for display engineers, even observers with perfect color vision are color blind at the highest spatial frequencies. This is indicated below in FIG. 3, where idealized spatial frequency responses of the human visual system are shown.
Here, luminance 17 refers to the achromatic contact of the viewed image, and chrominance 19 refers to the color content, which is processed by the visual system as isoluminant modulations from red to green, and from blue to yellow. The color difference signals R-Y and B-Y of video are rough approximations to these modulations. For most observers, the bandwidth of the chromatic frequency response is ½ that of the luminance frequency response. Sometimes, the bandwidth of the blue-yellow modulation response is even less, down to about ⅓ of the luminance. Sampling which comprises mapping of color elements from different image pixels to the subpixels of a display pixel triad may be referred to as sub-pixel sampling.
With reference to FIG. 4, in the horizontal direction of the display, there is a range of frequencies that lie between the Nyquist of the display pixel 16(display pixel=triad pixel, giving a triad Nyquist at 0.5 cycles per triad pixel) and the Nyquist frequency of the sub-pixels elements 10, 12 and 14 (0.5 cycles per subpixel=1.5 cycles/triad pixels). This region is shown as the rectangular region 20 in FIG. 4. The resulting sinc functions from convolving the high resolution image with a rect function whose width is equal to the display sample spacing is shown as a light dashed-dot curve 22. This is the most common approach taken for modeling the display MTF (modulation transfer function) when the display is an LCD.
The sinc function resulting from convolving the high-res source image with a rect equal to the subpixel spacing is shown as a dashed curve 24, which has higher bandwidth. This is the limit imposed by the display considering that the subpixels are rect in 1D. In the shown rectangular region 20, the subpixels can display luminance information, but not chromatic information. In fact, any chromatic information in this region is aliased. Thus, in this region, by allowing chromatic aliasing, we can achieve higher frequency luminance information than allowed by the triad (i.e., display) pixels. This is the “advantage” region afforded by using sub-pixel sampling.
For applications with font display, the black & white fonts are typically preprocessed, as shown in FIG. 5. The standard pre-processing includes hinting, which refers to the centering of the font strokes on the center of the pixel, i.e., a font-stroke specific phase shift. This is usually followed by low-pass filtering, also referred to as greyscale antialiasing.
The visual frequency responses (CSFs) shown in FIG. 3 are idealized. In practice, they have a finite falloff slope, as shown in FIG. 6A. The luminance CSF 30 has been mapped from units of cy/deg to the display pixel domain (assuming a viewing distance of 1280 pixels). It is shown as the solid line 30 that has a maximum frequency near 1.5 cy/pixel (display pixel), and is bandpass in shape with a peak near 0.2 cy/pixel triad. The R:G CSF 32 is shown as the dashed line, that is lowpass with a maximum frequency near 0.5 cy/pixel. The B:Y modulation CSF 34 is shown as the dashed-dotted LPF curve with a similar maximum frequency as the R:G CSF, but with lower maximum response. The range between the cutoff frequencies of the chroma CSF 32 and 34 and the luminance CSF 30 is the region where we can allow chromatic aliasing in order to improve luminance bandwidth.
FIG. 6A also shows an idealized image power spectra 36 as a 1/f function, appearing in the figure as a straight line with a slope of −1 (since the figure is using log axes). This spectrum will repeat at the sampling frequency. These repeats are shown for the pixel 38 and the subpixel 40 sampling rates for the horizontal direction. The one occurring at lower frequencies 38 is due to the pixel sampling, and the one at the higher frequencies 40 is due to the subpixel sampling. Note that the shapes change since we are plotting on a log frequency axis. The frequencies of these repeat spectra that extend to the lower frequencies below Nyquist are referred to as aliasing. The leftmost one is chromatic aliasing 38 since it is due to the pixel sampling rate, while the luminance aliasing 40 occurs at higher frequencies because it is related to the higher sub-pixel sampling rate.
In FIG. 6A, no prefiltering has been applied to the source spectra. Consequently, aliasing, due to the pixel sampling (i.e., chromatic aliasing), extends to very low frequencies 35. Thus even though the chromatic CSF has a lower bandwidth than the luminance CSF, the color artifacts may still be visible (depending on the noise and contrast of the display).
In FIG. 6B, we have applied the prefilter ( a rect function equal to three source image pixels), shown in FIG. 4 as a dashed-dotted line 22, to the source power spectrum, and it can be seen to affect the baseband spectrum 42 past 0.5 cy/pixel, causing it to have a slope steeper than −1 shown at 44. The repeats also show the effect of this prefilter. Even with this filter, we see that some chromatic aliasing (the repeated spectrum at the lower frequencies) occurs at frequencies 46 lower than the cut-off frequency of the two chrominance CSFs 32a and 34a. Thus it can be seen that simple luminance prefiltering will have a difficult time removing chromatic aliasing, without removing all the luminance frequencies past 0.5 cy/pix (i.e., the “advantage” region).
Since we are relying on the visual system differences in bandwidth as a function of luminance or chrominance to give us a luminance bandwidth boost in the “advantageous region” 20, one possibility is to design the prefiltering based on visual system models as described in C. Betrisey, et al (2000), “Displaced filtering for patterned displays,” SID Symposium digest, 296–299, hereby incorporated herein by reference and illustrated in FIG. 7.
This technique ideally uses different prefilters depending on which color layer, and on which color subpixel the image is being sampled for. Thus there are 9 filters. They were designed using a human visual differences model described in X. Zhang and B. Wandell (1996) “A spatial extension of CIELAB for digital color image reproduction,” SID Symp. Digest 731–734, incorporated herein by reference and shown in the FIG. 7. This was done offline, assuming the image is always black & white. In the final implementation, rect functions rather than the resulting filters are used in order to save computations. In addition, there is still some residual chromatic error that can be seen because the chromatic aliasing extends down to lower frequencies than the chromatic CSF cutoff (as seen in FIG. 6B).
However, the visual model used does not take into account the masking properties of the visual system which cause the masking of chrominance by luminance when the luminance is at medium to high contrast levels. So, in larger fonts the chromatic artifacts, which lie along the edges of the font, are masked by the high luminance contrast of the font. However, as the font size is reduced the luminance of the font reduces, and then the same chromatic artifacts become very visible (at very small fonts for example, the b/w portion of the font disappears, leaving only a localized color speckle).